week 1.

Lecture 1.  `The Room is Not Still''

Class intros and plane. 

\dot x = - \nabla V (x)
vs
\ddot x = - \nabla V(x).

gradient flow vs symplectic gradient
(Hamiltonian) flows

Some Morse Theory.

perhaps some control theory

Lecture 2. 

Prep for Rafael's Floer theoretic lectures:
More  Morse theory.

Various other numerics relating topology and dynamics.
The Lefshetz fixed point formulae and the Poincare-Hopf theorem.

More on  Hamilton's equations. Arnol'd's conjectured inequalities.



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week 2.  

student talk:  Rafael speaks. 

Lecture 3.    Some  Control theory. 
 Poisson brackets.
Poisson, symplectic, and contact manifolds. 
Maximum principle.  Legendre transformation.
SubRiemannian kinetic energy.  Geodesic and sR geod flows
as Hamiltonian flows.  Heis group.   Intro to Reeb paper of Yves (?)

Lecture 4.   Prep for Alejandro.  
Dichotomy of integrable/ non-integrable.  Nilpotentization.
Carnot groups. 





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week 3.   

student talk. John Pelias.  

Lecture 5.   Intro N-body problem.  Symmetries and reduction.
Shape space.  
The (Painleve-Wintner) problem of infinite spin. Horizontal lifts.
Reconstruction.

Lecture 6.  Center manifold plus Lojaseiwicz
gradient inequality to solve
the problem of infinite spin 

 

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week 4.  

student talk:  Cheyenne?   

Lecture 7.    Finishing infinite spin.  On to page 5 of
Richard Schwartz's paper.  ... 


Lecture 8.  Greg Laughlin's problems.  The balancing stick.
The falling cat.  Control with delay.  

 
*********

week 5. 

Lecture 9.  The balanced stick and GS687 (?)

Lecture 10.   


to be cont'd

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